## Abstract

The stability condition of (the four-dimensional Friedmann universe)*(a compact internal space) (F^{4}*K^{D}) is presented for a class of higher-dimensional theories, in which the effective potential depends only on a scale length of the internal space. The Candelas-Weinberg model (i.e. one-loop quantum correction+a cosmological constant Lambda ), eleven-dimensional supergravity+ Lambda , Einstein-Yang-Mills theory and six-dimensional Einstein-Maxwell theory are classified into this class. It is shown that the F^{4}*K^{D} solution is stable against small perturbations in the above models. The stability against non-linear perturbation is also investigated. The author finds that the stable F^{4}*K^{D} solution is an attractor for a finite range of initial conditions if the proper volume of the universe is increasing with time.

Original language | English |
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Article number | 017 |

Pages (from-to) | 233-247 |

Number of pages | 15 |

Journal | Classical and Quantum Gravity |

Volume | 3 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1986 |

Externally published | Yes |

## ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)